A005044

[franktaw at netscape.net]

This sequence, 0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 
10, ..., has the comment "Also the number of ways in which n empty 
casks, n casks half-full of wine and n full casks can be distributed to 
3 persons in such a way that each one gets the same number of casks and 
the same amount of wine [Alcuin]."  I think this comment applies to the 
sequence shifted left by 3 (i.e., without the 3 initial zeros).  E.g.,  
for n=2, one can give 2 people one full and one empty, and the 3rd gets 
two half-full.

Franklin T. Adams-Watters

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